📚 Year 9 OCR Additional Mathematics: Glossary & Terminology Quick Reference Guide | Year 9 OCR 进阶数学：词汇术语速记指南
Mastering the terminology of Additional Mathematics is the first step to building confidence in solving complex problems. This guide provides clear bilingual definitions and mnemonics for key terms you will encounter in Year 9 OCR Additional Maths, helping you memorise them quickly and effectively.
掌握进阶数学的术语是建立解题信心的第一步。这份指南以双语清晰定义了你在 Year 9 OCR 进阶数学中会遇到的关键词汇，并提供速记技巧，助你高效记忆。
1. Algebraic Fundamentals | 代数基础
Variable: A symbol, usually a letter such as x or y, that represents an unknown or changeable numerical value.
变量： 一个符号，通常是 x 或 y 等字母，代表未知或可变的数值。
Coefficient: The number multiplied by a variable in an algebraic term. For example, in 7x, 7 is the coefficient.
系数： 代数项中乘以变量的数。例如，在 7x 中，7 是系数。
Constant: A fixed numerical value that does not change; it appears as a standalone number in an expression, such as 5 in 2x + 5.
常数： 一个固定的数值，不会改变；它在表达式中作为独立数字出现，如 2x + 5 中的 5。
Expression: A combination of numbers, variables and operators (+, −, ×, ÷) without an equals sign, e.g., 3x² − 2y + 7.
表达式： 由数字、变量和运算符（+、−、×、÷）组成的式子，不含等号，例如 3x² − 2y + 7。
Like Terms: Terms that contain exactly the same variable(s) raised to the same power(s); they can be combined by adding or subtracting their coefficients.
同类项： 包含相同变量且对应指数完全相同的项；可通过系数相加减进行合并。
Simplify: To rewrite an expression in its most compact form by collecting like terms and performing operations.
化简： 通过合并同类项并进行运算，将表达式改写成最简形式。
2. Solving Equations and Inequalities | 解方程与不等式
Equation: A mathematical statement showing that two expressions are equal, indicated by an equals sign (=).
方程： 表明两个表达式相等的数学陈述，用等号（=）连接。
Linear Equation: An equation in which the highest power of the variable is 1, producing a straight line graph, e.g., 2x + 3 = 11.
线性方程： 变量的最高次数为 1 的方程，其图像为一条直线，如 2x + 3 = 11。
Quadratic Equation: An equation where the highest power of the variable is 2, typically written as ax² + bx + c = 0.
二次方程： 变量最高次数为 2 的方程，通常写作 ax² + bx + c = 0。
Root / Solution: A value that, when substituted for the variable, makes the equation true.
根 / 解： 代入变量后能使方程成立的数值。
Inequality: A statement comparing two expressions using symbols: < (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to).
不等式： 使用 <（小于）、>（大于）、≤（小于等于）、≥（大于等于）符号比较两个表达式的陈述。
Solve: To find the value(s) of the variable that satisfy an equation or inequality.
解（动词）： 求出使方程或不等式成立的变量值。
3. Sequences and Patterns | 数列与规律
Sequence: An ordered list of numbers following a specific rule or pattern, e.g., 2, 5, 8, 11, …
数列： 按照特定规则或模式排列的一列数，例如 2, 5, 8, 11, …
Term: Each individual number in a sequence; often referred to by its position, such as the 1st term, 2nd term, etc.
项： 数列中的每一个数；通常根据位置称为第 1 项、第 2 项等。
nth Term: A formula that allows you to calculate the term at any position n in a sequence without listing all previous terms.
第 n 项公式： 允许你直接计算数列中任意位置 n 的项的公式，无需列出前面所有项。
Arithmetic Sequence: A sequence where the difference between consecutive terms is constant, known as the common difference d.
等差数列： 相邻两项的差为常数的数列，该常数称为公差 d。
Common Difference: The fixed amount added (or subtracted) to each term to get the next term in an arithmetic sequence.
公差： 等差数列中，为得到下一项而每次加上（或减去）的固定数值。
Fibonacci Sequence: A special sequence where each term is the sum of the two preceding ones; it starts 1, 1, 2, 3, 5, 8, …
斐波那契数列： 一种特殊的数列，从 1, 1 开始，之后每一项都是前两项之和：1, 1, 2, 3, 5, 8, …
4. Functions and Graph Interpretation | 函数与图像解读
Function: A rule that assigns exactly one output value to each input value; often written as f(x) = …
函数： 一种对应规则，每个输入值恰好对应一个输出值；常写作 f(x) = …
Graph: A visual representation of the relationship between variables, usually plotted on coordinate axes.
图像： 变量之间关系的可视化表示，通常绘制在坐标轴上。
Linear Function: A function whose graph is a straight line, with a constant rate of change (gradient).
线性函数： 图像为一条直线的函数，其变化率（斜率）恒定。
Quadratic Function: A function of the form f(x) = ax² + bx + c, whose graph is a parabola.
二次函数： 形如 f(x) = ax² + bx + c 的函数，其图像是一条抛物线。
Parabola: The U-shaped (or inverted U-shaped) curve that represents a quadratic function.
抛物线： 表示二次函数的 U 形（或倒 U 形）曲线。
Turning Point: The point on a parabola where the graph changes direction; it can be a maximum or a minimum.
转折点/顶点： 抛物线上图像改变方向的点；可以是最大值点或最小值点。
Intercept: The point where a graph crosses an axis; the y-intercept is where x = 0, the x-intercept is where y = 0.
截距： 图像与坐标轴的交点；y 轴截距是 x = 0 时的点，x 轴截距是 y = 0 时的点。
5. Trigonometry | 三角学
Hypotenuse: The longest side of a right‑angled triangle, opposite the right angle.
斜边： 直角三角形中最长的边，对着直角。
Opposite Side: The side opposite the angle of interest in a right‑angled triangle.
对边： 直角三角形中对着所关心的角的那条边。
Adjacent Side: The side next to the angle of interest, other than the hypotenuse.
邻边： 直角三角形中紧邻所关心的角、且不是斜边的那条边。
Sine (sin): In a right‑angled triangle, the ratio of the length of the opposite side to the hypotenuse.
正弦 (sin)： 直角三角形中，对边长度与斜边长度的比值。
Cosine (cos): The ratio of the length of the adjacent side to the hypotenuse.
余弦 (cos)： 直角三角形中，邻边长度与斜边长度的比值。
Tangent (tan): The ratio of the length of the opposite side to the adjacent side.
正切 (tan)： 直角三角形中，对边长度与邻边长度的比值。
SOHCAHTOA: A mnemonic for remembering the trigonometric ratios: Sine = Opposite / Hypotenuse, Cosine = Adjacent / Hypotenuse, Tangent = Opposite / Adjacent.
SOHCAHTOA： 记忆三角比的口诀：正弦 = 对边 / 斜边，余弦 = 邻边 / 斜边，正切 = 对边 / 邻边。
Angle of Elevation: The angle measured upwards from the horizontal line to the line of sight when viewing an object above.
仰角： 从水平线向上测量到瞄准上方物体的视线之间的夹角。
Angle of Depression: The angle measured downwards from the horizontal line to the line of sight when viewing an object below.
俯角： 从水平线向下测量到瞄准下方物体的视线之间的夹角。
6. Geometry and Measurement | 几何与测量
Area: The amount of space inside a two‑dimensional shape, measured in square units (e.g., cm², m²).
面积： 二维形状内部的空间大小，以平方单位（如 cm²、m²）计量。
Perimeter: The total distance around the outside of a shape.
周长： 图形外部边界一圈的总长度。
Volume: The amount of space occupied by a three‑dimensional object, measured in cubic units (e.g., cm³, m³).
体积： 三维物体所占据的空间大小，以立方单位（如 cm³、m³）计量。
Circumference: The perimeter of a circle; the total distance around it.
圆周： 圆的周长，即绕圆一周的长度。
Radius: The distance from the centre of a circle to any point on its circumference; half of the diameter.
半径： 从圆心到圆周上任意一点的距离；是直径的一半。
Diameter: A straight line passing from side to side through the centre of a circle; twice the radius.
直径： 穿过圆心、两端在圆周上的线段；是半径的两倍。
Pi (π): The constant ratio of a circle’s circumference to its diameter, approximately 3.14159.
圆周率 (π)： 圆的周长与直径的固定比值，约为 3.14159。
Pythagoras’ Theorem: a² + b² = c² (where c is the hypotenuse)
勾股定理：a² + b² = c²（其中 c 为斜边）
7. Coordinate Geometry | 坐标几何
Coordinates: An ordered pair (x, y) that specifies the position of a point on the Cartesian plane.
坐标： 一个有序对 (x, y)，用于确定点在笛卡尔平面上的位置。
Midpoint: The point exactly halfway between two given points; its coordinates are the averages of the x‑coordinates and y‑coordinates: ((x₁ + x₂)/2, (y₁ + y₂)/2).
中点： 位于两点正中间的点；其坐标为两点 x 坐标和 y 坐标的平均值：((x₁ + x₂)/2, (y₁ + y₂)/2)。
Distance Formula: The length between two points (x₁, y₁) and (x₂, y₂) given by √[(x₂ − x₁)² + (y₂ − y₁)²].
距离公式： 两点 (x₁, y₁) 与 (x₂, y₂) 之间的距离，由 √[(x₂ − x₁)² + (y₂ − y₁)²] 给出。
Gradient (Slope): A measure of how steep a line is, calculated as the vertical change divided by the horizontal change (rise over run).
梯度（斜率）： 衡量一条线陡峭程度的量，计算为纵向变化除以横向变化（对边比邻边）。
y‑intercept: The point where a line crosses the y‑axis; its x‑coordinate is 0. In y = mx + c, c is the y‑intercept.
y 轴截距： 直线与 y 轴相交的点；其 x 坐标为 0。在 y = mx + c 中，c 即为 y 轴截距。
Equation of a straight line: y = mx + c (m = gradient, c = y‑intercept)
直线方程：y = mx + c（m 为斜率，c 为 y 轴截距）
8. Vectors | 向量
Vector: A quantity that has both magnitude (size) and direction; often represented by an arrow or a column of numbers.
向量： 既有大小（长度）又有方向的量；通常用箭头或一列数字表示。
Scalar: A quantity that has magnitude only, with no direction (e.g., speed, distance).
标量： 只有大小而无方向的量（如速率、路程）。
Magnitude: The length or size of a vector; always a non‑negative value.
模长： 向量的长度或大小；始终为非负值。
Column Vector: A way of writing a vector using vertical notation, e.g., (a, b) written as a 2×1 matrix with a on top and b on bottom, often displayed in text as (a b) stacked.
列向量： 用垂直形式书写向量的方法，例如将 (a, b) 写成上下两行，上方为 a、下方为 b。
Resultant Vector: The single vector that has the same effect as two or more vectors added together.
合向量： 两个或多个向量相加后得到的总向量，效果等同于这些向量的综合影响。
Parallel Vectors: Vectors that have the same direction or are exact opposites; they are scalar multiples of each other.
平行向量： 方向相同或恰好相反的向量；彼此互为标量倍数。
9. Probability and Statistics | 概率与统计
Probability: A measure of how likely an event is to occur, expressed as a number between 0 (impossible) and 1 (certain).
概率： 事件发生可能性的度量，用 0（不可能）到 1（必然）之间的数表示。
Sample Space: The set of all possible outcomes of an experiment, often listed between curly brackets.
样本空间： 一项试验所有可能结果的集合，常用花括号列出。
Event: A specific outcome or set of outcomes that we are interested in; a subset of the sample space.
事件： 我们关注的特定结果或结果集合；是样本空间的子集。
Theoretical Probability: The probability of an event calculated by assuming all outcomes are equally likely: P(event) = number of favourable outcomes / total number of outcomes.
理论概率： 假定所有结果等可能时计算出的事件概率：P(事件) = 有利结果数 / 总结果数。
Mean: The average of a set of numbers, found by adding all values and dividing by the count of values.
平均数（均值）： 一组数据的平均值，将所有数值相加后除以数据个数求得。
Median: The middle value in an ordered list of numbers; for an even count, it is the mean of the two middle numbers.
中位数： 按顺序排列的一组数中居于中间位置的值；若个数为偶数，则取中间两数的平均值。
Mode: The value that appears most frequently in a data set.
众数： 数据集中出现次数最多的值。
Range: A measure of spread calculated as the difference between the largest and smallest values.
极差： 衡量数据分散程度的量，为最大值与最小值之差。
10. Number: Surds and Indices | 数系：根式与指数
Rational Number: A number that can be expressed as a fraction a/b where a and b are integers and b ≠ 0; its decimal form terminates or recurs.
有理数： 可以表示为分数 a/b 的数，其中 a、b 为整数且 b ≠ 0；其小数形式要么有限，要么循环。
Irrational Number: A number that cannot be written as a simple fraction; its decimal expansion is non‑terminating and non‑repeating, e.g., π, √2.
无理数： 无法写成简单分数的数；其小数展开无限且不循环，如 π、√2。
Surd: An irrational root of a rational number, often left in square root form, such as √3, 2√5.
根式/不尽根： 有理数的无理方根，通常保留平方根形式，例如 √3、2√5。
Simplify a Surd: To rewrite a surd so that the number under the root sign has no perfect square factors, e.g., √50 = 5√2.
化简根式： 将根式改写，使得根号内的数不含完全平方因子，如 √50 = 5√2。
Rationalise the Denominator: The process of eliminating a surd from the denominator of a fraction by multiplying the numerator and denominator by a suitable value.
分母有理化： 通过分子分母同乘适当的数，使分母不再含有根式的过程。
Standard Form (Scientific Notation): A way of writing very large or very small numbers in the form a × 10ⁿ, where 1 ≤ a < 10 and n is an integer.
标准形式（科学记数法）： 书写极大或极小数字的方法，形式为 a × 10ⁿ，其中 1 ≤ a < 10，n 为整数。
Significant Figures: The digits in a number that carry meaning contributing to its precision; rules determine how to round to a given number of significant figures.
有效数字： 数字中携带意义并影响精度的那些数位；有规则规定如何舍入到指定有效数字位数。
11. Ratios, Proportions and Percentages | 比、比例与百分比
Ratio: A comparison of two or more quantities of the same kind, often written as a:b or a to b.
比： 两个或多个同类量的比较，常写作 a:b 或 a 比 b。
Proportion: An equation stating that two ratios are equal; also describes the relationship between quantities that scale together.
比例： 说明两个比相等的等式；也可描述数量间同时缩放的关系。
Direct Proportion: Two quantities are directly proportional if their ratio is constant; when one increases, the other increases by the same factor.
正比： 如果两个量的比值恒定，则它们成正比；一个量乘以几倍，另一个也乘以相同的倍数。
Inverse Proportion: Two quantities are inversely proportional if their product is constant; when one increases, the other decreases proportionally.
反比： 如果两个量的乘积恒定，则它们成反比；一个量增大，另一个量比例化减小。
Percentage: A fraction expressed with a denominator of 100, denoted by the symbol %.
百分比： 分母为 100 的分数，用 % 符号表示。
Percentage Increase/Decrease: The change in a quantity expressed as a percentage of the original amount; (change / original) × 100%.
百分比增减： 量的变化表示为原值的百分比；(变化量 / 原值) × 100%。
Multiplier: A number used to scale a quantity directly; for a p% increase, the multiplier is 1 + p/100; for a decrease, it is 1 − p/100.
乘数/倍率： 用于直接缩放一个量的数；增长 p% 时乘数为 1 + p/100，减少时为 1 − p/100。
12. Exam Command Words and Memory Tricks | 考试指令词与记忆口诀
Evaluate: ‘Find the numerical value of’ – substitute given numbers and calculate.
求值： “求出数值”——代入给定数字并进行计算。
Simplify: Reduce an expression to its simplest form; do not solve, just make it neater.
化简： 将表达式化为最简形式；不要解方程，只需整理整洁。
Expand: Multiply out brackets to write an expression without brackets, e.g., 3(x + 2) = 3x + 6.
展开： 将括号乘开，写成无
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